The correct answer is USD 5.86, which is calculated using the binomial option pricing model with risk-neutral probabilities.

Key Calculation Steps:

1. Risk-neutral probability of up move: 57.61% (given from previous question)

2. Final node payoffs:

   • Node [D]: max(0, 52-72) = 0
   • Node [E]: max(0, 52-48) = 4
   • Node [F]: max(0, 52-32) = 20

3. Backward induction:

   • Node [B]: (0.5761×0 + 0.4239×4) × exp(-0.12×3/12) = 1.65 (intrinsic value = 0, so no early exercise)
   • Node [C]: (0.5761×4 + 0.4239×20) × exp(-0.12×3/12) = 10.46 (intrinsic value = 12, so early exercise at 12)
   • Node [A]: (0.5761×1.65 + 0.4239×12) × exp(-0.12×3/12) = 5.86 (intrinsic value = 2, so no early exercise)

Why other options are incorrect:

• A (USD 2.00): This is the intrinsic value at node A (max(0, 52-50) = 2), but doesn't account for time value
• B (USD 5.23): This would be the value if it were a European put option (exercisable only at expiration)
• D (USD 6.04): This value doesn't match the calculated no-arbitrage price using the binomial model